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Scientific experts of course require that statistical significance be established at a p-value of .05, which is a 95 percent confidence interval. The 95 percent confidence interval is completely unrelated to the burden of proof in a civil case — the “preponderance of the evidence.”

We nonetheless frequently hear plaintiffs maintain that “the burden of proof is only a preponderance of the evidence — 51 percent. Defendant’s experts insist on proof to a p-value of .05, or 95 percent certainty. That’s higher than the burden of proof in court. The court should exclude testimony by experts who insist on a p-value of .05 to establish statistical significance.”

That’s hogwash, of course, but the mathematical issue is sufficiently complex that few courts have analyzed it in detail. To our eye, the Federal Judicial Center’s Reference Manual On Scientific Evidence gives the best explanation why this plaintiff’s assertion reflects a “common error” that courts must reject:

A common error made by lawyers, judges, and academics is to equate the level of alpha [standard for statistical significance] with the legal burden of proof. Thus, one will often see a statement that using an alpha of .05 for statistical significance imposes a burden of proof on the plaintiff far higher than the civil burden of a preponderance of the evidence (i.e., greater than 50%) ….

This claim is incorrect, although the reasons are a bit complex and a full explanation would require more space than is feasible here. Nevertheless, we sketch out a brief explanation: First, alpha does not address the likelihood that a plaintiff’s disease was caused by exposure to the agent; the magnitude of the association bears on that question. Second, significance testing only bears on whether the observed magnitude of association arose as a result of random chance, not on whether the null hypothesis is true. Third, using stringent significance testing to avoid false positive error comes
at a complementary cost of inducing false negative error. See DeLuca v. Merrell Dow Pharms., Inc., 911 F.2d 941, 947 (3d Cir. 1990). Fourth, using an alpha of .5 would not be equivalent to saying that the probability the association found is real is 50%, and the probability that it is a result of random error is 50%. Statistical methodology does not permit assessments of those probabilities. [Citing many authorities]

Federal Judicial Center, Reference Manual On Scientific Evidence at 358 n.67 (2d ed. 2000) (citations omitted) (emphasis added).

Look no further for helpful authority. When you confront this argument, there’s the easy and compelling response.